Related papers: Stable Homology-Based Cycle Centrality Measures

Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…

Research on the robustness of the Internet has gained critical importance in the last decades because more and more individuals, societies and firms rely on this global network infrastructure for communication, knowledge transfer, business…

Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant topological signals across distinct systems. In geometry and…

Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…

We present a novel set of methods for analyzing coverage properties in dynamic sensor networks. The dynamic sensor network under consideration is studied through a series of snapshots, and is represented by a sequence of simplicial…

Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…

We derive a composite centrality measure for general weighted and directed complex networks, based on measure standardisation and invariant statistical inheritance schemes. Different schemes generate different intermediate abstract measures…

High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…

Identifying influential nodes and edges in directed networks remains a fundamental challenge across domains from social influence to biological regulation. Most existing centrality measures face a critical limitation: they either discard…

Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…

We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is…

Node centrality is one of the integral measures in network analysis with wide range of applications from socio-economic to personalized recommendation. We argue that an effective centrality measure should undertake stability even under…

This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…

Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…

Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires…

Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify…

Much of the past work in network analysis has focused on analyzing discrete graphs, where binary edges represent the "presence" or "absence" of a relationship. Since traditional network measures (e.g., betweenness centrality) utilize a…

This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…

While representation learning has yielded a great success on many graph learning tasks, there is little understanding behind the structures that are being captured by these embeddings. For example, we wonder if the topological features,…

In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…